Ground state of solutions for a class of fractional Schrödinger equations with critical Sobolev exponent and steep potential well
Sign Up to like & getrecommendations! Published in 2017 at "Mathematical Methods in The Applied Sciences"
DOI: 10.1002/mma.4527
Abstract: In this paper, we study the following fractional Schrodinger equations: (−△)αu+λV(x)u=κ|u|q−2u|x|s+β|u|2α∗−2u,u∈Hα(RN),N⩾3,(1) where (−△)α is the fractional Laplacian operator with α∈(0,1),2≤q≤2α,s∗=2(N−s)N−2α≤2α∗=2NN−2α, 0≤s≤2α, λ>0, κ and β are real parameter. 2α∗ is the critical Sobolev exponent. We… read more here.
Keywords: sobolev; sobolev exponent; critical sobolev; ground state ... See more keywords
On Kirchhoff type equations with critical Sobolev exponent
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DOI: 10.1016/j.jmaa.2018.02.023
Abstract: We study the following Brezis-Nirenberg problem of Kirchhoff type $$ \left\{\aligned &-(a+b\int_{\Omega}|\nabla u|^2dx)\Delta u = \lambda|u|^{q-2}u + \delta |u|^{2}u, &\quad \text{in}\ \Omega, \\ &u=0,& \text{on}\ \partial\Omega, \endaligned \right. $$ where $\Omega\subset \bbr^4$ is a bounded… read more here.
Keywords: critical sobolev; equations critical; type equations; sobolev exponent ... See more keywords
Ground state and multiple solutions for the fractional Schrödinger–Poisson system with critical Sobolev exponent
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DOI: 10.1016/j.nonrwa.2017.12.003
Abstract: Abstract In this paper, we study the following doubly singularly perturbed fractional Schrodinger–Poissonsystem with critical Sobolev exponent e 2 α ( − Δ ) α u + V ( x ) u + ϕ u… read more here.
Keywords: ground state; critical sobolev; multiple solutions; sobolev exponent ... See more keywords
Nonlocal Elliptic Systems Involving Critical Sobolev-Hardy Exponents and Concave-convex Nonlinearities
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DOI: 10.11650/tjm/190109
Abstract: In this paper, a system of fractional elliptic equation is investigated, which involving fractional critical Sobolev-Hardy exponent and concave-convex terms. By means of variational methods and analytic techniques, the existence and multiplicity of positive solutions… read more here.
Keywords: concave convex; elliptic systems; sobolev hardy; critical sobolev ... See more keywords